The present invention relates to a triangular-pyramidal cube-corner retroreflective sheeting having a novel structure. More minutely, the present invention relates to a triangular-pyramidal cube-corner retroreflective sheeting in which triangular-pyramidal reflective elements having a novel structure are arranged in the closest-packed state.
Still more minutely, the present invention relates to a cube-corner retroreflective sheeting constitute of triangular-pyramidal cube-corner retroreflective elements (hereafter referred to as triangular-pyramidal reflective elements or merely, elements) useful for signs including traffic signs and construction work signs, license plates of automobiles and motorcycles, safety materials of clothing and life preservers, markings of signboards, and reflectors of visible-light, laser-beam, and infrared-ray reflective sensors.
Still further minutely, the present invention relates to a triangular-pyramidal cube-corner retroreflective sheeting characterized in that triangular-pyramidal cube-corner retroreflective elements protruded beyond a common base plane (X-Xxe2x80x2) are faced each other and arranged on the base plane (X-Xxe2x80x2) in the closest-packed state by sharing one base edge on the base plane (X-Xxe2x80x2), the base plane (X-Xxe2x80x2) is a common plane including many base edges (x, x, . . . ) shared by the triangular-pyramidal reflective elements, the two triangular-pyramidal reflective elements faced each other constitute an element pair having substantially same shape faced so as to be respectively substantially symmetric to planes (Y-Yxe2x80x2, Y-Yxe2x80x2, . . . ) vertical to the base plane (X-Xxe2x80x2) including many shared base edges (x, x, . . . ) on the base plane (X-Xxe2x80x2), the triangular-pyramidal reflective elements are constituted of substantially same hexagonal or triangular lateral faces (prism faces) (faces c1 and c2) using the shared base edges (x, x, . . . ) as one sides and substantially same quadrangular lateral faces (faces a1 and b1 and faces a2 and b2) substantially orthogonal to the face c1 or the face c2 by using two upper sides of the face c1 or c2 starting with apexes (H1 and H2) of the triangular-pyramidal reflective elements as one sides and sharing one ridge line of the triangular-pyramidal reflective elements and using the ridge line as one side, and when assuming the height from the apexes (H1 and H2) of the triangular-pyramidal reflective elements up to the base plane (X-Xxe2x80x2) including the base edges (x, x, . . . ) of the hexagonal or triangular lateral faces (faces c1 and c2) of the triangular-pyramidal reflective elements as (h), the height from the apexes (H1 and H2) of the triangular-pyramidal reflective elements up to a substantially horizontal plane (Z-Zxe2x80x2) including base edges (z and w) of other lateral faces (faces a1 and b1 and faces a2 and b2) of the triangular-pyramidal reflective elements as (h0), the intersection between a vertical line from the apexes (H1 and H2) of the triangular-pyramidal reflective elements to the base plane (X-Xxe2x80x2) and the base plane (X-Xxe2x80x2) as P, the intersection between an optical axis passing through the apexes (H1 and H2) and the base plane (X-Xxe2x80x2) as Q, and moreover, expressing distances from the intersections (P) and (Q) up to planes (Y-Yxe2x80x2, Y-Yxe2x80x2, . . . ) including the base edges (x, x, . . . ) shared by the triangular-pyramidal reflective elements and vertical to the base plane (X-Xxe2x80x2) as p and q, and assuming the angle formed between the optical axis and the vertical plane (Y-Yxe2x80x2) as (xcex8), the above h and h0 are not substantially equal and meet the following expression (1).
                              0.5          ⁢          R                ⁢                  xe2x80x83                ≦                  xe2x80x83                ⁢                  h                      h            0                          ≦                  xe2x80x83                ⁢                  1.5          ⁢          R                                    (        1        )            
(In the above expression, R is defined by the following expression.)   R  =                    sin        ⁢                  (                                    35.2644              *                        -            θ                    )                    +              1.2247        ⁢                  xe2x80x83                ⁢        sin        ⁢                  xe2x80x83                ⁢        θ                    sin      ⁢              (                              35.2644            *                    -          θ                )            
(In the above expression, it is assumed that when the value of the above (pxe2x88x92q) is negative, xcex8 takes a negative (xe2x88x92) value.)
A retroreflective sheeting for reflecting incoming light toward a light source has been well known so far and the sheeting using its retroreflective characteristic is widely used in the above fields. Particularly, a retroreflective sheeting using the retroreflective principle (theory) of a cube-corner retroreflective element such as a triangular-pyramidal reflective element is extremely superior to a conventional retroreflective sheeting using micro glass beads in retroreflectivity and its purpose has been expanded year by year because of its superior retroreflective performance.
However, though a conventionally-publicly-known triangular-pyramidal retroreflective element shows a preferable retroreflectivity when the angle formed between the optical axis of the element {axis passing through the apex of the triangular pyramid of the triangular-pyramidal retroreflective element equally separate from three lateral faces (faces a, b, and c)} constituting a triangular-pyramidal cube-corner retroreflective element and intersecting each other at an angle of 90xc2x0 and an incident light (the angle is hereafter referred to as entrance angle) is kept in a small range, the retro-reflectivity rapidly deteriorates as the entrance angle increases (that is, the entrance angularity deteriorates).
Moreover, the reflection principle (theory) of a triangular-pyramidal retroreflective element uses internal total reflection caused on the interface between air and a transparent medium constituting the triangular-pyramidal reflective element when light is emitted to air from the transparent medium at a specific angle {critical angle (xcex1c)} or more. The critical angle (xcex1c) is shown as the following expression by a refractive index (n) of a transparent medium constituting a triangular-pyramidal reflective element and a refractive index (n0) of air.
      sin    ⁢          xe2x80x83        ⁢          α      c        =            n      0        n  
In this case, it is allowed to consider the refractive index (n0) of air is almost equal to 1 and constant. Therefore, the critical angle (xcex1c) decreases as the value of the refractive index (n) of the transparent medium increases and light easily reflects from the interface between the transparent medium and air. When using a synthetic resin for a transparent medium, the critical angle (xcex1c) shows a comparatively large value of approx. 42xc2x0 because most synthetic resins have a refractive index of approx. 1.5.
Light incoming to the surface of a retroreflective sheeting using the above triangular-pyramidal reflective element at a large entrance angle reaches the interface between the triangular-pyramidal reflective element and air at a comparatively small angle from a lateral face (reflecting surface) of the reflective element after passing through the triangular-pyramidal reflective element. When the comparatively small angle is smaller than the critical angle (xcex1c), the light passes through the back of the element without totally reflecting from the interface. Therefore, a retroreflective sheeting using a triangular-pyramidal reflective element has a disadvantage that it is generally inferior in entrance angularity.
However, because a triangular-pyramidal retroreflective element is able to reflect light in the light incoming direction over almost entire surface of the element, reflected light does not reflect by emanating to a wide angle due to spherical aberration like a micro-glass-bead reflective element. However, in practical use, the narrow divergence angle of retroreflected light easily causes a trouble that the light emitted from a head lamp of an automobile does not easily reach eyes of a driver present at a position separate from the optical axis of the light such as eyes of the driver when the light is retroreflected from a traffic sign. The above trouble more frequently occurs particularly when an automobile approaches a traffic sign because the angle (observation angle) formed between a light entrance axis and an axis connecting a driver and a reflection point (that is, the observation angularity deteriorates).
Many proposals have been made so far for the above cube-corner retroreflective sheeting, particularly for a triangular-pyramidal cube-corner retroreflective sheeting and various improvements and studies are made.
For example, Jungersen""s U.S. Pat. No. 2,481,757 discloses a retroreflective sheeting constituted by arranging retroreflective elements of various shapes on a thin sheeting and a method for manufacturing the sheeting. Triangular-pyramidal reflective elements disclosed in the above U.S. patent include a triangular-pyramidal reflective element in which the apex is located at the center of a base-plane triangle and the optical axis does not tilt and a triangular-pyramidal reflective element in which the apex is not located at the center of a base-plane triangle but the optical axis tilts. More-over, it is described in the U.S. patent to efficiently reflect light toward an approaching automobile. Furthermore, it is described that the size of a triangular-pyramidal reflective element, that is, the depth of the element is {fraction (1/10)}xe2x80x3 in (2,540 xcexcm) or less. Furthermore, FIG. 15 in the U.S. patent illustrates a triangular-pyramidal reflective element whose optical axis tilts in the plus (+) direction similarly to the case of a preferred mode of the present invention. The tilt angle (xcex8) of the optical axis is estimated as approx. 6.5xc2x0 when obtaining it from the ratio between the longer edge and shorter edge of the base-triangular plane of the illustrated triangular-pyramidal reflective element.
However, the above Jungersen""s U.S. patent does not specifically disclose a very small triangular-pyramidal reflective element shown in the present invention or it does not disclose a size or an optical-axis tilt which a triangular-pyramidal reflective element must have in order to show superior observation angularity and entrance angularity.
Moreover, Stamm""s U.S. Pat. No. 3,712,706 discloses a retroreflective sheeting in which the so-called equilateral triangular-pyramidal cube-corner retroreflective elements in which shapes of their base-plane triangles are equilateral triangular and shapes of three other sides are right isosceles triangular are arranged on a thin sheeting so that their base planes are brought into the closest-packed state on a common plane. Stamm""s U.S. patent solves the problem that retroreflectivity is deteriorated due to increase of an entrance angle through mirror reflection by vacuum-coating the reflective surface of a reflective element with a metal such as aluminum and the above trouble that the light incoming at an angle of less than an internal total-reflection condition passes through the interface between elements and thereby, it does not retroreflect.
However, because the above Stamm""s proposal uses the mirror reflection principle (theory) as means for improving the angularity (wide angularity), the proposal easily causes the trouble that the appearance of an obtained retroreflective sheeting becomes dark or the reflective brightness easily deteriorates because a metal such as aluminum or silver used for the mirror surface is oxidized due to incoming water or air while it is used. Moreover, the proposal does not describe means for improving the angularity (wide angularity) by a tilt of an optical axis at all.
Moreover, Hoopman""s European Pat No. 137,736(B) discloses a retroreflective sheeting in which triangular-pyramidal cube-corner retroreflective elements with a tilted optical axis whose triangular base-plane is isosceles triangular are brought into the closest-packed state on a common plane. Moreover, it is described that the optical axis of a triangular-pyramidal cube-corner retroreflective element disclosed in the patent tilts in a negative (xe2x88x92) direction and its tilt angle approximately ranges between 7xc2x0 and 13xc2x0.
However, according to the relation between reflective brightness and optical-axis tilt examined by the present inventor et al. through the light tracing method, it is found that reflective brightness lowers as the tilt angle of a optical axis exceeds 4xc2x0 and further increases in a negative direction and particularly, the reflective brightness of a triangular-pyramidal reflective element whose optical axis exceeds 6xc2x0 in a negative direction extremely lowers. This may be because areas of three prism faces a, b, and c forming a triangular-pyramidal reflective element whose optical axis does not tilt are equal to each other but areas of faces a and b of an element whose optical axis tilts in a negative direction slowly decrease compared to the area of the face c of the element as the tilt angle of the element increases.
Moreover, Szczech""s U.S. Pat. No. 5,138,488 also discloses a retroreflective sheeting in which titled triangular-pyramidal cube-corner retroreflective elements whose base planes are isosceles triangular are arranged on a thin sheeting so that the base planes are brought into the closest-packed state. In the U.S. patent, optical axes of the triangular-pyramidal reflective elements tilt in the direction of a side shared by paired triangular-pyramidal reflective elements faced each other and it is specified that the tilt angle approximately ranges between 2xc2x0 and 5xc2x0 and the size of an element ranges between 25 and 100 xcexcm.
Furthermore, European Pat. No. 548,280(B1) corresponding to the above U.S. patent discloses that the distance between a plane including a common side of paired triangular-pyramidal cube-corner retroreflective elements and vertical to a common plane and the apex of the element is not equal to the distance between the intersection with the common plane of the optical axis of the element and the vertical plane, that is, the tilt of the optical axis may be either of positive (+) and negative (xe2x88x92) directions, and its tilt angle approximately ranges between 2xc2x0 and 5xc2x0, and the size of the element ranges between 25 and 100 xcexcm.
As described above, in the case of Szczech""s European Pat. No. 548,280(B1), the tilt of an optical axis approximately ranges between 2xc2x0 and 5xc2x0 including positive (+) and negative (xe2x88x92) directions. However, in the case of the tilt of the optical axis in the range of the Szczech""s invention, wide angularity, particularly entrance angularity is not adequately improved.
The conventionally-publicly-known triangular-pyramidal cube-corner retroreflective elements of Jungersen""s U.S. Pat. No. 2,481,757, Stamm""s U.S. Pat. No. 3,712,706, Hoopman""s European Pat. No. 137,736(B1), Szczech""s U.S. Pat. No. 5,138488 and European Pat. No. 548,280(B1) are common to each other in that base planes of many triangular-pyramidal reflective elements serving as a core of entrance and reflection of light are present on the same plane. Thus, every retroreflective sheeting constituted of triangular-pyramidal reflective elements whose base planes are present on the same plane is inferior in entrance angularity, that is, it has a disadvantage that retroreflective brightness suddenly deteriorates when an entrance angle of light to the triangular-pyramidal reflective element increases.
In general, not only high brightness, that is, level (magnitude) of reflective brightness of the light incoming from the front of a triangular-pyramidal cube-corner retroreflective sheeting but also wide angularity of the light are requested as basic optical characteristics of the sheeting and moreover, three performances such as observation angularity, entrance angularity, and rotational angularity are requested for the wide angularity.
As described above, every conventionally-publicly-known retroreflective sheeting constituted of triangular-pyramidal cube-corner retroreflective elements has been inferior in entrance angularity and observation angularity. However, the present inventor et al. found through light-tracing simulation that it is possible to improve the entrance angularity of a retroreflective sheeting constituted of triangular-pyramidal reflective elements by making the height (hxe2x80x2) from the plane (X-Xxe2x80x2) including many base edges (x, x, . . . ) shared by the triangular-pyramidal reflective elements set at symmetric positions each other up to the apexes (H1 and H2) of the elements substantially larger than the height (h) from the plane (Z-Zxe2x80x2) including base edges (z and w) of two faces (faces a and b) substantially orthogonal to the face c having one base edge shared by the triangular-pyramidal reflective elements as one side up to the apex of the reflective elements and applied a patent. (Japanese Patent Application No. 295907/1996).
Moreover, the present inventor et al. continued the study by light tracing simulation and found that it is also possible to improve the entrance angularity of a retroreflective sheeting constituted of two triangular-pyramidal reflective elements faced each other by making the height (hxe2x80x2) from the first plane (X-Xxe2x80x2) including base edges (x, x, . . . ) of lateral faces (faces c1 and c2) having base edges (x, x, . . . ) shared by the triangular-pyramidal reflective elements as one side up to the apexes (H1 and H2) of the triangular-pyramidal reflective elements substantially smaller than the height (h) from the substantially-horizontal second base plane (Z-Zxe2x80x2) including the base edges (z and w) of other lateral faces (faces a1 and b1 and faces a2 and b2) of the triangular-pyramidal reflective elements up to the apexes (H1 and H2) of the triangular-pyramidal reflective elements and applied a patent.
(Japanese Patent Application No. 330836/1997)
The present inventor et al. further continued the study that the improvement in the above two applied patents was achieved by minimizing the problem of relatively enlarging or contracting sizes of the lateral faces (faces c1 and c2) which had been conventionally caused by a tilt of an optical axis compared to other lateral faces (faces a1 and b1 and faces a2 and b2). As a result, we found that the ratio between the height (h) from the base plane (X-Xxe2x80x2) including common base edges (x, x . . . ) of the lateral faces c1 and c2 faced with the triangular-pyramidal reflective element pair up to the apexes (H1 and H2) of the element pair and the height (h0) from one horizontal plane (Z-Zxe2x80x2) including the base edges (z and w) of the two substantially-same-shaped lateral faces (faces a1 and b1 and faces a2 and b2) of the element pair up to the apexes (H1 and H2) of the element pair must be kept in a specific range shown by a tilt angle xcex8 of an optical axis and a specific relational expression and finished the present invention.
Therefore, the present invention relates to a triangular-pyramidal cube-corner retroreflective sheeting characterized in that triangular-pyramidal cube-corner retroreflective elements protruded beyond a common base plane (X-Xxe2x80x2) are faced each other and arranged in the closest-packed state by sharing one base edge on the base plane (X-Xxe2x80x2), the base plane (X-Xxe2x80x2) is a common plane including many base edges (x, x, . . . ) shared by the triangular-pyramidal reflective elements, the two triangular-pyramidal reflective elements faced each other constitute an element pair having substantially same shape faced so as to be respectively substantially symmetric to planes (Y-Yxe2x80x2, Y-Yxe2x80x2, . . . ) vertical to the base plane (X-Xxe2x80x2) including many shared base edges (x, x, . . . ) on the base plane (X-Xxe2x80x2), the triangular-pyramidal reflective elements are constituted of substantially same hexagonal or triangular lateral faces (faces c1 and c2) using the shared base edges (x, x, . . . ) as one sides and substantially same quadrangular lateral faces (faces a1 and b2 and faces a2 and b2) substantially orthogonal to the face c1 or the face c2 by using upper two sides of the face c1 or face c2 starting with apexes (H1 and H2) of the triangular-pyramidal reflective elements as one sides and sharing one ridge line of the triangular-pyramidal reflective elements and using the ridge line as one side, and when assuming the height from the apexes (H1 and H2) of the triangular-pyramidal reflective elements up to the base plane (X-Xxe2x80x2) including the base edges (x, x, . . . ) of the hexagonal or triangular lateral faces (face c1 and face c2) of the triangular-pyramidal reflective elements as (h), the height from the apexes (H1 and H2) of the triangular-pyramidal reflective elements up to a substantially horizontal plane (Z-Zxe2x80x2) including base edges (z and w) of other lateral faces (faces a1 and b2 and faces a2 and b2) of the triangular-pyramidal reflective elements as (h0), the intersection between a vertical line from the apexes (H1 and H2) of the triangular-pyramidal reflective elements to the base plane (X-Xxe2x80x2) and the base plane (X-Xxe2x80x2) as P, the intersection between an optical axis passing through the apexes (H1 and H2) and the base plane X-Xxe2x80x2) as Q, and moreover, expressing distances from the intersections (P) and (Q) up to planes (Y-Yxe2x80x2, Y-Yxe2x80x2, . . . ) including the base edges (x, x, . . . ) shared by the triangular-pyramidal reflective elements and vertical to the base plane (X-Xxe2x80x2) as p and q, and assuming the angle formed between the optical axis and the vertical plane (Y-Yxe2x80x2) as (xcex8), the above h and h0 are not substantially equal and meet the following expression (1).                               0.5          ⁢                      xe2x80x83                    ⁢          R                ≦                  h                      h            0                          ≦                  1.5          ⁢                      xe2x80x83                    ⁢          R                                    (        1        )            
(In the above expression, R is defined by the following expression.)   R  =                    sin        ⁢                  (                                    35.2644              *                        -            θ                    )                    +              1.2247        ⁢        sin        ⁢                  xe2x80x83                ⁢        θ                    sin      ⁢              (                              35.2644            *                    -          θ                )            
(In the above expression, it is assumed that when the value of the above (pxe2x88x92q) is negative, xcex8 takes a negative (xe2x88x92) value.)
The present invention is more minutely described below by properly referring to the accompanying drawings.